Question:
Prove that (Sin5x + sin3x)/(Cos5x + Cos3x) = tan 4x
Answer:
Given (Sin5x + sin3x)/(Cos5x + Cos3x)
= {2*sin (5x + 3x)/2 * cos (5x - 3x)/2}/{2*cos (5x + 3x)/2 * cos (5x - 3x)/2}
= {2*sin 4x * cos x}/{2*cos 4x * cos x}
= sin 4x/ cos 4x
= tan 4x
So, (Sin5x + sin3x)/(Cos5x + Cos3x) = tan 4x
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